Question

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at a height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm, the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is `N/100`, where N is an integer, the value of N is ..........

Answer 1

From the figure,

sin i = `15/(15 sqrt2) = 1/sqrt2`

and sin r = `15/sqrt(15^2 + 30^2)`

= `1/sqrt5`

n = `sin i/sin r`

= `sqrt(5/2)`

= 1.58

= `158/100`

Thus, N = 158.